M2488253 Mersenne number exponent details

Residue

Status

L-L

85DECD11D4DE409E

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	11.9417	67.1642%	2382500	85770100	0.6965	8.1983%	12.6382	69.8561%	2.6920%
PrimeNet	2⁵⁹	0.0309	62.7119%	10000	180000	0.0019	2.5356%	0.0328	63.6574%	0.9455%
GPU72	2⁶³	0.6414	65.0794%	11000	160000	0.0019	1.3808%	0.6433	65.5615%	0.4822%
Difference	+4	+11.3003	+2.0848%	+2371500	+85610100	+0.6946	+6.8175%	+11.9949	+4.2946%	+4.2946%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.9417

67.1642%

2382500

85770100

0.6965

8.1983%

12.6382

69.8561%

2.6920%

PrimeNet

2⁵⁹

0.0309

62.7119%

10000

180000

0.0019

2.5356%

0.0328

63.6574%

0.9455%

GPU72

2⁶³

0.6414

65.0794%

11000

160000

0.0019

1.3808%

0.6433

65.5615%

0.4822%

Difference

+11.3003

+2.0848%

+2371500

+85610100

+0.6946

+6.8175%

+11.9949

+4.2946%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2488253	389529429104347659985513	24	78.366	78273678179901252 2² × 3 × 5659 × 51197 × 22513877	2014-11-21	51197	22513877	29,778	0.1282	0.2304
2488253	55910285222055839015849983	26	85.531	11234847345116400747 3³ × 7 × 25409 × 31477 × 74323211	2014-11-21	31477	74323211	4,966,976	0.4102	0.7606

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2488253

389529429104347659985513

78.366

78273678179901252
2² × 3 × 5659 × 51197 × 22513877

2014-11-21

51197

22513877

29,778

0.1282

0.2304

2488253

55910285222055839015849983

85.531

11234847345116400747
3³ × 7 × 25409 × 31477 × 74323211

2014-11-21

31477

74323211

4,966,976

0.4102

0.7606

exponent	prime factors	composite factor	digits	bits*
2488253	389529429104347659985513 55910285222055839015849983	21778701483608656610004100716278432697267161296279	50	163.897

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.290%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.919%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.314%
2011-01-21T06:03:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.680%
2014-09-03T20:52:00	Jocelyn Larouche	Manual testing	120795	120795		-		-	-	0.012	-	-	1.053%
2014-11-21T01:38:00	mikr	MSI	2382500	85770100	12		389529429104347659985513 55910285222055839015849983	50	163.897	0.697	0.345	1.393	8.198%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	bezahar	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2022-03-10T05:53:01	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.062	-	-
2009-01-14T22:44:00	Sturle Sunde	giovanni.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-10T14:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.123	-	-
2013-01-14T11:53:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.395	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.102 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.102 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.102

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-14T02:28:00	SubPrime	c2d0	50000	5000000						3	0.276
2010-03-29T03:30:00	James Classen	towerofart	50000	5000000						3	0.276
2012-06-23T07:10:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.276
2014-02-12T05:54:00	Andy Incline	Office-PC	50000	5000000						3	0.276

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	bezahar	v4_computers	85DECD11D4DE409E	0.173

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

bezahar

v4_computers

85DECD11D4DE409E

0.173

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T09:19:21

kkmrkkblmbrbk

c4.xlarge

94C459E12E708F__

2017-11-06T10:51:45

Oliver Kruse

GTX-0

389529429104347659985513

55910285222055839015849983

94C459E12E708F__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 2382500, B2 = 85770100 (P-1 stage 2)

B1 = 2382500 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 120795 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront